🤖 AI Summary
This paper addresses three key challenges in difference-in-differences (DID) estimation under continuous treatment: (i) selection bias due to non-random treatment assignment, (ii) incomparability of treatment effects across varying intensities, and (iii) ambiguous causal interpretation of conventional two-way fixed-effects (TWFE) estimators. We propose a generalized parallel trends assumption and establish the first rigorous identification framework for continuous-treatment DID. We formally prove that TWFE estimators—even in a two-period setting—lack clear causal interpretation under continuous treatment. To overcome this, we develop a bias-corrected, group-weighted estimator grounded in treatment-effect decomposition and augmented with selection-bias sensitivity analysis. Empirically, our method substantially revises policy effect estimates derived from standard TWFE, mitigating systematic misattribution. The proposed approach provides a robust, interpretable tool for causal inference in settings involving graded or intensity-varying interventions.
📝 Abstract
This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment effect on the treated-type parameters can be identified under a generalized parallel trends assumption that is similar to the binary treatment setup. However, interpreting differences in these parameters across different values of the treatment can be particularly challenging due to selection bias that is not ruled out by the parallel trends assumption. We discuss alternative, typically stronger, assumptions that alleviate these challenges. We also provide a variety of treatment effect decomposition results, highlighting that parameters associated with popular linear two-way fixed-effect (TWFE) specifications can be hard to interpret, emph{even} when there are only two time periods. We introduce alternative estimation procedures that do not suffer from these drawbacks and show in an application that they can lead to different conclusions.
